Question 15

# If a and b are negative, and c is positive, which of the following statement/s is/are true?I) $$a - b < a - c$$ II) if $$a < b$$, then $$\frac{a}{c} < \frac{b}{c}$$III) $$\frac{a}{b} > \frac{a}{c}$$

Solution

I) $$a-c$$ is negative as $$a$$ is negative and $$c$$ is positive. Thus, the value of $$a-c$$ will be smaller than $$a$$(since more negative is added to a negative number). $$a-b$$ can be negative or positive depending upon the value of $$a$$ and $$b$$, but it can be concluded that this number will be greater than $$a$$(since a positive number is added to a negative number). Thus, $$(a-c)<(a-b)$$. Thus, the statement I is false.

II) Given $$a<b$$, $$\frac{a}{c}<\frac{b}{c}$$ as $$c$$ is positive and $$a < b$$. Therefore, statement II is true

III) $$a$$ is negative and $$b$$ is negative, this implies $$\frac{a}{b}$$ is positive. $$a$$ is negative and $$c$$ is positive, this implies $$\frac{a}{c}$$ is negative. Therefore, $$\frac{a}{b}>\frac{a}{c}$$. Statement III is true

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